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Molecular Diversity (2006) 10: 415–427DOI: 10.1007/s11030-006-9018-4 c Springer 2006

Full-length paper

On an aspect of calculated molecular descriptors in QSAR studies of quinolone

antibacterials

Payel Ghosh1, Megha Thanadath2 & Manish C. Bagchi1,∗

1 Drug Design, Development and Molecular Modelling Division, Indian Institute of Chemical Biology, 4 Raja S.C. Mullick

Road, Jadavpur, Calcutta 700032, India; 2 K.V.M College of Information Technology, Cherthala, Alleppey, Kerala, India

(∗ Author for correspondence, E-mail: [email protected], Tel.: +91 33 2473 3491/3493/0493/6793, Fax: +91 33 2473

5197, +91-33-2472 3967)

Received 25 October 2005; Accepted 18 January 2006

Key words: quantitative structure activity relationship, quinolone antibacterials, molecular descriptors, intermolecular similarity,PERL programming, ridge regression

Summary

The re-emergence of tuberculosis infections, which are resistant to conventional drug therapy, has steadily risen in the last

decade and as a result of that, fluoroquinolone drugs are being used as the second line of action. But there is hardly any

study to examine specific structure activity relationships of quinolone antibacterials against mycobacteria. In this paper, an

attempt has been made to establish a quantitative structure activity relationship modeling for a series of quinolone compounds

against Mycobacterium fortuitum and Mycobacterium smegmatis. Due to lack of sufficient physicochemical data for the anti-

mycobacterial compounds, it becomes very difficult to develop predictive methods based on experimental data. The present paper

is an effort for the development of QSARs from the standpoint of physicochemical, constitutional, geometrical, electrostatic and

topological indices. Molecular descriptors have been calculated solely from the chemical structure of N-1, C-7 and 8 substituted

quinolone compounds and ridge regression models have been developed whichcan explain a better structure-activity relationship.

Consideration of an intermolecular similarity analysis approach that led to a successful computer program development in

PERL language has been used for comparing the influence of various molecular descriptors in different data subsets. The

comparison of relative effectiveness of the calculated descriptors in our ridge regression model gives rise to some interesting

results.

Introduction

The greatest threats to tuberculosis control are the associa-

tion of this disease with the HIV epidemic and the increase

in resistance to the most effective anti-tuberculosis drugs.The global increase of multi-drug resistant M. tuberculosis

strains and intolerance of first line anti-tuberculosis drugs

such as isoniazide, rifampicin, pyrazinamide and ethamb-

utol may cause major problems and necessitate modifica-

tion of standard therapy regimen [1]. Recently developed

drugs like 6-fluoro-4-quinolone-3-carboxylic acids seem to

be very effective in cases of severe intolerance of first line

anti-tuberculosis medication [2, 3]. Of these fluoroquinolone

drugs, sparfloxacin seems to be the most potent agent be-

cause of its broad-spectrum efficacies, both in vitro and

in vivo, better than those of ofloxacin and ciprofloxacin

against mycobacterial infections [4, 5]. Developments in the

quinolone family for producing more active agents against

gram-positive organisms and mycobacteria are being con-

tinued with substitutions at N-1 and C-7 as well as at the

8 position of the quinolone ring with a view to obtain the

relationship between structural modification at these posi-

tions and activity against mycobacteria [6, 7]. These agentswere evaluated for their activities against Mycobacterium

fortuitum and Mycobacterium smegmatis, as the activities

of the compounds against these two organisms were used

for a measure of Mycobacterium tuberculosis activity. But

there is hardly any study to examine specific structure ac-

tivity relationships of the quinolone anti-bacterials against

mycobacteria. Quantitative Structure Activity Relationship

(QSAR) studies are based on the premise that biological

response is a function of the chemical structure. Thus, the

significant parameters of chemical structure have been de-

fined in numerical terms for the use in the development

of specific QSAR models [8]. Computer-aided drug design

methods, in general, have been rapidly developed in the



417

Table 1. Quinolone substrates and their activities considered in the present study

MIC Values(µg/mL) MIC Values(µg/mL)Comp No. R 1 R 7 X M.fort M.smeg

Comp No. R 1 R

7X M.fort M.smeg

1 NHN

CH 0.06 0.25 2

N NH3C

CH 0.06 0.25

3 NHN

H3C

CH 0.06 0.25

4 NHN

H 3C

H 3C

CH 0.06 0.13

5 NH N

E t

CH 0.13 0.25

6 N NEt CH 0.06 0.13

7 N NiPr

CH 0.25 0.258

N NiPrCH2

CH 1.0 0.25

9 N NBun

CH 1.0 0.5 10

N

H 2 N

CH 0.03 0.25

11

N

M e N H C H 2

CH 0.25 0. 5 12

N

EtNHCH2

CH 0.5 0.5

13

N

PrNHCH2iCH 0.25 0.5

14

N

(Me)2 NC H2

CH 0.13 0.5

15

N

H2 N CH 2 CH 3

CH 0.03 0.0616

F

F

NHN CH 0.25 0.5

17

F

F

N NH3C CH 0.25 0.518

F

F

NHN

H 3C

CH 0.13 0.5

(Continued on next page)

In the present study, an attempt has been made to classify the

set of 69 quinolone compounds using a criterion of structural

similarity. This criterion keeps a close relationship between

the molecules belonging to each one of the classes and their

biological activity. To study the structural similarity, it is es-

sential to build a mathematical space where chemical struc-

tures are pictured as vectors, whose components describe

topological features proper of their chemical nature. It is

expected that these chemical structures will be distributed

in mathematical space according to their structural charac-

teristics, so that, we could find neighborhoods of similar

molecules. For a well-defined structural space, it is expected

that molecules with similar biological activity will be in the

same neighborhood of structural similarity [22]. A set of

well-chosen descriptors such as physicochemical, geomet-

rical, constitutional, electrostatic and topological descriptors

may be used as variables. These descriptors arise from the

graph theoretical studies, which are often used as a powerful



418

Table 1. (Continued )

19

F

F

NHN

H3C

H3C

CH 0.25 0.5 20

F

F

NHN

Et

CH 0.25 1.0

21

F

F

N NEt

CH 0.5 1.0

22

F

F

N NiPr

CH 0.5 1.0

23

F

F

N NiPrCH2

CH 2.0 4.024

F

F

N NBun

CH 1.0 2.0

25

F

F

N

H2 N

CH 0.13 0.1326

F

F

N

MeNHCH2

CH 0.13 0.25

27

F

F

N

EtNHCH 2

CH 0.5 0.528 CH2CH3

NHN

CH 0.5 2.0

29 CH2CH3 NHN

H3C

CH 1.0 2.0 30 CH2CH3

NHN

H3C

H3C

CH 0.13 1.0

31 CH2CH3 N NEt

CH 0.25 0.532 CH2CH3

N

H2 N

CH 1.0 4.0

33 CH2CH3

N

MeNHCH 2

CH 2.0 8.034

NH N CH 0.03 0.13

35 NHN

H3C

CH 0.03 0.0636

NHN

H 3C

H3C

CH 0.06 0.06


tool in the rational drug design. Thus, quantitative molecu-

lar similarity analysis was performed to sub-group the set of

quinolone antibacterials by similarity. An atom pair oriented

approach for the inter-molecularsimilarityusing the principle

of Carhart and development of a suitable computer program

in PERL script [23] by our group, will definitely help us to

subdivide the entire database into three categories – (a) the

whole set of 69 compounds, (b) compoundshaving more than50% similarity with Sparfloxacin, a known fluoroquinolone

tuberculostatic drug and (c) compounds having more than

60% similarity with that of Sparfloxacin. The chemical struc-

ture of Sparfloxacin with its biological activity values in MIC

(µg/mL) against M. fortuitum and M. smegmatis are given in

the Figure 1.

The computer program has mainly two tasks- the first

module is to generate the atom pairs for each of the quinolone

derivativesand to determine shortestpath separation. The sec-ond module deals with the calculation of the intermolecular



419


37 N NEt

CH 0.13 0.1338

N

H2 N

CH 0.06 0.13

39

N

MeNHCH2

CH 0.13 0.2540

NH N

CH 1.0 4.0

41 NHN

H3C

CH 0.5 2.042

NHN

H 3C

H3C

CH 0.05 2.0

43 N NEt

CH 1.0 4.0

44

N

H2 N

CH 1.0 2.0

45

N

MeNHCH2

CH 2.0 8.046

NH N

CH 0.5 2.0

47 NHN

H3C

CH 0.25 1.048 NHN

H 3C

H3C

CH 0.13 0.5

49 N NEt

CH 0.5 2.0

50

N

H2 N CH 1.0 1.0

53 NHN

H3C

CBr 0.03 0.0654

NHN

H 3C

H3C

CBr 0.03 0.06

55 N NEt

CBr 0.03 0.0656

N

H2 N

CBr 0.03 0.06

57

N

MeNHCH2

CBr 0.03 0.06 58 NH N

COMe 0.03 0.03


similarity between any two compounds based on the atom

pairs along with the shortest path separation as determined

in the first module. This program is unique in the sense that

it can determine the intermolecular similarity between any

two chemical structures by using simply the positions of the

atoms and bonds of the concerned structures as specified in

the input format. The intermolecular similarity of all the 69

quinolone antibacterials considered in our present study with

that of Sparfloxacin was generated using the above program

and are represented in Table 2.

The computational approach for the generation of the

atom pairs andsimilarity calculation are given below whereas

the main program in PERL script is given in the supple-

mentary section. An atom pair is a substructure composed



420


59 NHN

H3C

COMe 0.03 0.0360

NHN

H 3C

H3C

COMe 0.03 0.03

61 N NEt

COMe 0.03 0.0362

N

H2 N

COMe 0.03 0.03

63

N

MeNHCH2

COMe 0.03 0.0364

NH N

N 0.03 0.06

65 NHN

H3C

N 0.03 0.06

66 NHN

H 3C

H3C

N 0.03 0.06

67 N NEt

N 0.03 0.0668

N

H2 N

N 0.03 0.06

69

N

MeNHCH2

N 0.03 0.06

Figure 1. Sparfloxacin with MIC= 0.06 & 0.13 against M. fort & M. smeg,

respectively

of two non-hydrogen atoms, i and j, and their interatomicseparation,

<atom description i>

− <separation> − <atom description j>

To find the interatomic separation, which is the shortest path

distance between any two atoms in a chemical structure, we

represent the structure in the form of a tree, in which each

level of the tree structure corresponding to a particular atom

shows the number of the neighbors that atom is attached to.

Thus, the program in this direction will definitely help us tocompute atom pairs from a specific input format. The first line

of the input should be a forward slash (/) which represents

the start of the input. The format for the next line following

the forward slash is given as:

< symbol><atom name i> (position of the

neighboring atoms separated by commas (, ))

The<symbol>caneitherbe“#”or“∼” dependingon whether

the atom is having a double bond or single bond respectively.

Molecular similarity, S (s, t ), between any two structures,

s and t may be calculated as,

S (s, t ) =2

d (s) + d (t )

distincttypes i

of atom pairs

MIN[n(i, s), n(i, t )]

where d (s) and d (t ) represents the total number of atom pairs

in s and t respectively.

Theoretical molecular descriptors calculation

The molecular descriptors used in the present paper are of

4 categories viz. (a) physicochemical, (b) constitutional and

geometrical, (c) electrostatic and (d) topological descriptors.The physicochemical descriptors consist of the molecular



421

Computational approach for the generation of atom pairs from two chemical structures

If Yes

Similarity calculation for the two compounds

Whether input data files of the chemical structuretogether with the bonds and neighbours and atomic

symbol for compounds exit

Shortest path calculation from each atom to all other atoms using tree structure

representation where levels of the tree are treated as the array positions.

Identification of the initial and terminal atoms from the input data filefor obtaining atom descriptions

Classification of each atom from its environment consisting of bonds

and neighbouring atom(s) associated with it.

Terminate program

If No

Print the obtained results in the atom-pair format

Store the calculated atom pairs of two chemical structures infiles, comp1.txt in the 1st iteration and comp2.txt in nextiteration for further analysis.

Go to step1 for thedeterminationof atom

pair for second structure

Exit the program

Calculate the no. of atom-pairs from the files, viz. comp1.pl and comp2.pl

Count the similar type of atom-pairs separately for each compound

Compare the count of each atom pair type from both thestructures and take the minimum of the number of occurrences

Obtain the total count of these minimum numbers of occurrences

Substitute these values in calculating structural similarity between two compounds

Print the results, i.e. the molecular similarity betweentwo compounds in percentage

Exit the program

descriptors like AlogP98 value, AMR value, buffer solubil-

ity, polarizability, vapour density, water solubility etc. De-

scriptors like formal charges, fraction of rotatable bonds,

number of rigid bonds, number of rings, number of charged

groups etc. form the constitutional descriptors. The three-

dimensional or shape descriptors (3-D) are more complex,

encoding information about the three dimensional aspects

of molecular structure. The electrostatic descriptors include



422

Table 2. Structural similarity of quinolone derivatives against

Sparfloxacin

Comp Similarity with C omp Similarity with

no. Sparfloxacin(%) no. Sparfloxacin (%)

1 61.16 2 55.753 69.91 4 79.09

5 64.58 6 54.05

7 57.06 8 55.03

9 49.21 10 60.86

11 61.45 12 58.16

13 59.52 14 60.36

15 57.18 16 46.43

17 43.30 18 52.89

19 57.65 20 49.11

21 42.23 22 44.62

23 43.27 24 38.19

25 46.17 26 47.21

27 44.39 28 49.13

29 56.57 30 63.13

31 44.25 32 48.18

33 50.15 34 45.13

35 51.78 36 57.06

37 46.36 38 47.79

39 50.20 40 55.66

41 61.94 42 67.99

43 50.07 44 55.05

45 57.18 46 59.29

47 67.99 48 77.09

49 52.40 50 59.29

51 59.53 52 64.01

53 73.40 54 82.58

55 56.79 56 64.01

57 64.75 58 63.16

59 71.88 60 79.89

61 56.08 62 63.44

63 63.49 64 47.79

65 54.05 66 59.81

67 43.72 68 46.90

69 49.66

charge polarization, local dipole index, maximum positiveand negative charges, general polarity parameters, relative

charge etc., whereas the topological descriptors are the

biggest set of molecular descriptors which may again be sub-

divided into two classes- topostructural and topochemical

descriptors. The topostructural descriptors encode informa-

tion strictly on the neighborhood and connectivity of atoms

within the molecule while the topochemical descriptors en-

code information related to both the topology of the molecule

and chemical nature of atoms and bonds within it.

In our present paper, we have used the software pack-

age PreADMET [24], which is a web based application

for predicting ADME data and building drug-like libraryusing insilico method. Two commercially available edition

of PreADMET are available, (i) standard and (ii) profes-

sional. This program can calculate about 955 molecular de-

scriptors including constitutional, geometrical, topological,

electrostatic and physicochemical descriptors, which has

been developed in response to need for rapid prediction of

drug likeliness and ADME/Toxicity data. The input file may

be created either by drawing the chemical structure or using

an appropriateSMILES notation of the compound concerned.

A total number of 444 molecular descriptors were calculated

for our present investigation using PreADMET program and

prior to model development, the set of calculated descrip-

tors was reduced from 444 to 294. The reduction in the de-

scriptors was either due to keeping a constant value for (or

nearly) all of the compounds, or those that were perfectly

correlated with another class of descriptors. Table 3 repre-

sents the symbols of the calculated molecular descriptors

used in our present study together with their corresponding

groups.

Statistical analysis

Multivariate regression analysis (MRA), one of the oldest

data reduction methodologies, continues to be widely used

in QSAR [25] as it does not impose any restriction on the

type and number of graphical invariants used in structure-

property activity studies. For a valid statistical significance

of the MRA, it is necessary to restrict the maximal number of

descriptors, which will depend on the number of compounds

investigated [26, 27]. In order to avoid ambiguities in the

interpretation of regression, only few parameters, or ideally

a single parameter may be used. But the structure activity

relationship of chemical compounds requires a huge number

of physicochemical and molecular descriptors. Considera-

tion of theoretical molecular descriptors like constitutional,

geometric, electrostatic and topologicaldescriptors has found

wide applications in quantitative structure activity relation-

ship modeling [28, 29]. To establish such a relationship be-

tween activity and structural descriptors of the quinolone

compounds under consideration, it is essential to develop a

regression or an input-output model. Multiple linear regres-

sion and partial least squares are common for development of

linear QSAR models while methods such as artificial neural

network areused in thecase of non-linear modeling.Topolog-icalindices are in particularinescapable in the development of

successful multiple regression analysis leading to the QSAR

of rational drug design. The present study regarding QSAR of

quinolone antibacterials involves a huge number of various

types of topological as well as physicochemical descriptors.

Conventional regression i.e. ordinary least squares (OLS)

does not produce reliable models when the number of de-

scriptors exceeds the number of observations [30, 31]. In

this situation, the alternate and appropriate statistical meth-

ods that may be considered are ridge regression (RR) [32],

principal component regression (PCR) [33] and partial least

squares (PLS) [34–36]. All the above three linear statisticalmethods are very useful and have a wide applicability when



423

Table 3. List of molecular descriptors used in this study

Descriptor classes Descriptor names

Constitutional Descriptors No. amino groups primary, No. amino groups secondary, No. amino groups tertiary,

No. ester groups, No. halogen atoms, Molecular weight, No. Total atoms, No.

Rotatable bonds, Fraction of Rotatable bonds, No. Rigid bonds, No. Rings, No.

Aromatic rings, No. single bonds, No. aromatic bonds, No. H-bond acceptors, Ratio

donors to acceptor.

Geometrical Descriptors 2D-VDW surface, 2D-VDW volume, 2D-VSA hydrophobic, Fraction of 2D-VSA hydrophobic, 2D-VSA

hydrophobic sat, 2D-VSA hydrophobic unsat, 2D-VSA other,

2D-VSA polar, Fraction of 2D-VSA polar, 2D-VSA Hbond acceptor, 2D-VSA Hbond

donor, 2D-VSA Hbond all, Fraction of 2D-VSA Hbond, Fraction of 2D-VSA

chargable groups, Topological PSA.

Electrostatic Descriptors Max negative charge, Max positive hydrogen charge, Total negative charge, Total

positive charge, Total absolute atomic charge, Charge polarization, Local dipole index,

Polarity parameter, Relative positive charge, Relative negative charge, PPSA1(Partial

Positive Surface Area 1st type), PPSA2, PPSA3, PNSA1(Partial Negative Surface

Area 1st type), PNSA3, DPSA1(Difference in Charged Partial Surface Area), DPSA2,DPSA3, FPSA1(Fractional charged partial positive surface area 1st type), FPSA2,

FPSA3, FNSA1(Fractional charged partial negative surface area 1st type), FNSA3,

WPSA1 (Surface weighted charged partial positive surface area 1st type), WPSA2,

WPSA3, WNSA1 (Surface weighted charged partial negative surface area 1st type),

WNSA3, RPCS (Relative positive charge surface area), RNCS (Relative negative

charge surface area), Hydrophobic SA – MPEOE, Positive charged polar SA –

MPEOE, Negative charged polar SA – MPEOE, SADH1 (Surface area on donor

hydrogens 1st type), SADH2 (Surface area on donor hydrogens 2nd type), SADH3

(Surface area on donor hydrogens 3rd type), CHDH1 (Charge on donatable hydrogens

1st type), CHDH2, CHDH3, SCDH1 (Surface weighted charged area on donor

hydrogens 1st type), SCDH2, SCDH3, SAAA1 (Surface weighted charged area

on acceptor atoms 1st type), SAAA2, SAAA3, CHAA1 (Charge on acceptors atoms 1st

type), CHAA2, CHAA3, SCAA1 (Surface weighted charged area on acceptor atoms

1st type), SCAA2, SCAA3, HRNCS, HRNCG.

Topological Descriptors Total structure connectivity index, Chi 0 (Simple zero order chi index), Chi 1, Chi 2,

Chi 3 path (Simple third order path chi index), Chi 3 cluster (Simple 3rd order cluster

chi index), Chi 4 path, Chi 5 path, Chi 4 path/cluster (Simple 4th order path/cluster chi

index), VChi 0 (Valance zero order chi index), VChi 1, VChi 2, VChi 3 path (Valance

3rd order path chi index), VChi 4 path, VChi 3 cluster, VChi 4 path/cluster, VChi 5

path, Kier shape 1 (encodes the degree of cyclicity in the graph, decreases as graph

cyclicity increases), Kier shape 2 (encodes the degree of central branching in the

graph,decreases as the degree of central branching increases.), Kier shape 3 (encodes

the degree of separated branching in the graph,increases as the degree of separation in

branching increases.), Kier alpha 1 (1st Order Kappa Alpha Shape Index), Kier alpha

2, Kier alpha 3, Kier flexibility, Kier symmetry index, Kier steric descriptor, Delta Chi

0 (Delta zero order chi index), Delta Chi 1, Delta Chi 2, Delta Chi 3 path, Delta Chi 3

cluster, Delta Chi 4 path, Delta Chi 4 cluster, Chi 4 path/cluster, Delta Chi 5 path,

Difference chi 0 (Difference simple zero order chi index), Difference chi 1, Difference chi 2,

Difference chi 3, Difference chi 4, Difference chi 5, IC (information content

index), BIC (bond information content), CIC (complementary information content), SIC

(structural information content), IAC total (total information index of atomic

composition), I adj equ (Information index based on the vertex adjacency matrix

equality), I adj mag (Information index based on the vertex adjacency matrix

magnitude), I adj deg equ (Information index based on the degree adjacency matrix

equality), I adj deg mag, I dist equ (Information index based on the distance matrix

equality), I dist mag (Information index based on the distance matrix magnitude),




424


Descriptor classes Descr ip to r names

I edge adj equ (Information index based on the edge adjacency matrix equality),

I edge adj mag (Information index based on the edge adjacency matrix magnitude),

I edge adj deg equ, I edge adj deg mag, I edge dist equ, I edge dist mag,

Wiener index (Half-sum of the off-diagonal elements of the distance matrix of a

graph), Hyper Wiener index, Harary index (Half-sum of the off-diagonal elements of

the reciprocal molecular distance matrix), 1st Zagreb (1st Zegreb index), 2nd Zagreb,

Quadratic index, Rouvray index, 2-MTI (Schultz Molecular Topological Index (MTI)),

2-MTI prime (Schultz MTI by valence vertex degrees), Gutman MTI, Graph diameter,

Graph radius, Graph Petitjean, Eccentric connectivity index, Eccentric adjacency

index, Platt number, Odd-even index, Vertex degree-distance index, Ring degree-

distance index, Balaban index JX, Balaban index JY, Xu (Xu index), Superpendentic

index, Unipolarity distance matrix, Centralization distance matrix,

Dispersion distance matrix, SC-0 (Subgraph Count Index of order 0), SC-1, SC-2,

SC-3 path, SC-3 cluster, SC-4 path, SC-4 cluster, SC-4 path/cluster, SC-5 path, SC-6

path, SC-7 path, SC-8 path, SC-9 path, SC-10 path, Solvation chi 0 (Solvation zeroorder chi index), Solvation chi 1, Solvation chi 2, Solvation chi 3 path, Solvation chi 3

cluster, Solvation chi 4 path, Solvation chi 4 cluster, Solvation chi 4 path/cluster,

Solvation chi 5 path, VS-0 (Valence Shell Count of order 0), VS-1, VS-2, VS-3, VS-4,

VS-5, Molecular walk count 2, Molecular walk count 3, Molecular walk count 4,

Molecular walk count 5, Path/walk 2, Path/walk 3, Path/walk 4, Path/walk 5, Narumi

ATI (Narumi simple topological index (log)), Narumi HTI (Narumi harmonic

topological index), Narumi GTI(Narumi geometric topological index), Pogliani index,

Ramification index, Degree complexity, Graph vertex complexity, Graph distance

complexity, Graph distance index, Mean square distance index, Mean distance

deviation, Edge Wiener index, Edge Hyper Wiener index, Edge MTI, Edge Gutman

MTI, Edge connectivity index, E-state SsCH3, E-state SssCH2, E-state SdsCH, E-state

SsssCH, E-state SaasC, E-state SssssC, E-state SsssNH, E-state SdO, E-state

S hydrophobic, E-state S hydrophobic unsat, E-state S polar, E-state

S hbond donor, E-state S negative charged group, E-state SHssNH2, E-state

SHdsCH, E-state SHCHnX, E-state SH hydrophobic, E-state SH polar, E-state

SaaCH, E-state SdssC, E-state SssNH2, E-state SsssN, E-state SsOHl, E-state SsF, E-

state S hydrophobic sat, E-state S none, E-state S hbond acceptor, E-state

S positive charged group, E-state SHsssNH, E-state SHaaCH.

Physicochemical Descriptors Polarizability Miller, SKlogP value, Water solubilityl, Vapor pressure, Buffer solubility,

SK MP, AMR value (Calculated molecular refractivity index), Polarizability MPEOE,

SKlogS value, SKlogPvp, SKlogS buffer, SK BP, AlogP98 value, AlogP98 002C,

AlogP98 006C, AlogP98 008C, AlogP98 024C, AlogP98 026C, AlogP98 038C, AlogP98

040C, AlogP98 047H, AlogP98 051H, AlogP98 053H, AlogP98 057O, AlogP98 067N, AlogP98 071N,

AlogP98 073N, AlogP98 075N, AlogP98 094Br, AlogP98 084F, AlogP98

001C, AlogP98 003C, AlogP98 005C, AlogP98 011C, AlogP98 029C, AlogP98 046H,AlogP98 050H, AlogP98 052H, AlogP98 060O, AlogP98 066N, AlogP98 068N.

the number of independent variables greatly exceed the num-

ber of observations and when the independent variables are

highly inter-correlated. Each of these methods makes use of

the entire available pool of independent variables as opposed

to selecting a subset, which introduces bias and may result

in the elimination of important parameters from our studies.

From the works of Miller [31] and Friedman [38], it is also

known that data subsetting is less effective than those meth-

ods that retain all of the independent variables and use other

approaches to deal with the rank deficiency. Among the three

statistical methods involving RR, PCR and PLS, it is found

that RR is the best among the three methods, and this is used

extensively in multiple comparative studies [18, 38–40]. For

this reason, the models based on the large set of constitutional

and geometric, electrostatic and topological descriptors were

developed using the RR methodology. RR, like PCR, trans-

forms thedescriptorsto their principal components (PCs) and

uses the PCsas descriptors. However, unlike PCR, RR retains

all of the PCs, and “shrinks” them differentially according to

their eigenvalues. The RR vector of regression coefficients,



425

b, is given by

b = (XTX+k I)−1XTY

where X is the matrix of descriptors, Y is the vector of observed activities, I is an identity matrix, and k is a non-

negative constant known as the “ridge” constant. If k = 0,

RR reduces to conventional OLS regression. Thus, the Ridge

Regression (RR) method has been applied in our dataset of

quinolone compounds and models have been developed ac-

cordingly for various sets of molecular descriptors and an

effective comparison among the RR models for the above

descriptor classes have been made and discussed in the next

section.

Results and discussion

QSAR studies have been performed using the theoretical

molecular descriptors, calculated from the PreADMET

Molecular Descriptor Calculation package and experimen-

tally derived biological activity data of the quinolone

derivatives both for M. fortuitum and M. smegmatis and the

ridge regression analysis is given in the Table 4. We have con-

sidered all of the 69 quinolone compounds, i.e. N1 and C7 as

well as 8 substituted derivatives of quinolone antibacterials

and different subsets to be used in the statistical analysis.

Further subsetting of the above biological activity data has

been considered by us utilizing molecular similarity analysis

for an effective comparison of the results obtained from the

RR analysis. Similarity analysis performed by us enhance

the scope of sub grouping the data into further two categories

viz., (i) compoundshaving 50%or more inter molecularsimi-

larity with Sparfloxacin, the fluoroquinolone drug used as an

anti-tuberculostatic agent and (ii) compounds having 60%

and more similarity with the drug. So, four cases of ridge

regression models were developed as for example the com-

plete set of 69 quinolone compounds; 51 sets of N1 and C7

substituted quinolone derivatives; and two other groups of

data consisting of 48 and 22 compounds arising out of the

above similarity analysis. To calculate the molecular sim-

ilarity between any two compounds, we have developed acomputer program in PERL script and the main utility of

this program is that it can generate the whole sets of atom-

pairs of each compound andcalculate the structural similarity

afterwards from the input files containing the minimum in-

formation, i.e. the positions of atoms and bonds of respective

compounds.

Thus it is evident that the structural similarity oriented

sub grouping of the entire data set has actually arranged the

quinolone compounds activity-wise for it is known that the

structurally similar compounds may possess similar activity.

From the above sub grouping of Table 4, we can study the

pattern of influence of any descriptor class on activity in thisproposed QSAR model of quinolone compounds that help us

to arrive at some conclusions.Tostudythe pattern of influence

of the descriptor classes, it is necessary to compare the R2

values in our ridge regression model. The total RR analysis

was done using the NCSS software package [41].

The above table provides the regression summary for QSAR

of the quinolone derivatives in cases of Mycobacterium for-

tuitum and Mycobacterium smegmatis. For the complete set

of 69 compounds, the RR model only with the topological

descriptors has R2 values of 0.8357 and 0.8200 for M. for-

tuitum and M. smegmatis respectively and the addition of

other theoretical descriptors like constitutional and geomet-

rical and electrostatic indices have contributed significantly

towards a better R2 value thus improving the model quality.

From the Table, it is seen that the influence of the above de-

scriptors when considered alone result in inferior models. For

the same set of compounds, the RR model based on physic-

ochemical descriptors appears to be very poor compared to

the topological descriptors derived model. When we considerthe group of the first 51 compounds in Table 1 excluding the

derivatives with the substitution at 8 position, we see that

the RR models based on topological descriptors alone can

fit the data very well. The fit is clearly much better com-

pared to the physicochemical model. Even the electrostatic

descriptors can describe the model better with R2 values of

0.7380 and 0.6850 for the case of M. fortuitum and M. smeg-

matis respectively than the physicochemical descriptors with

the R2 values of 0.6947 and 0.6408 against those respec-

tive mycobacteria. If we take all the calculated molecular

descriptors like topological, electrostatic and constitutional

and geometrical indices into account, we get an excellent fit

with the value of R2 being 0.9021 and 0.8830 for M. fortu-

itum and M smegmatis respectively. In the third case, where

48 quinolone compounds were considered on the basis of

50% or more similarity cases, it is worthwhile to mention

that this dataset gives overall improved values of R2 than

the previous datasets. Here also the topological descriptors

alone can describe the model much better than the physico-

chemical property based model and the combination of all the

calculated descriptors such as constitutional and geometrical,

electrostatic and topological indices contribute to a more sig-

nificant model development. This trend is also continued in

the last subset of 22 quinolone compounds possessing 60%

or more structural similarity with sparfloxacin. The pattern of influence of these structural descriptors seems to be the same

as in the previous cases when compared to the physicochem-

ical descriptors. So it is evident from the QSAR reported in

Table 3 that the calculated molecular descriptors could pro-

vide a better quality predictive model for N-1, C-7 and 8 sub-

stituted quinolone derivatives. The physicochemical property

based QSPR studies resulted in much inferior models. The

QSAR models based on molecular descriptors that are calcu-

lated solely from the chemical structure can be used as more

reliable models for predicting the potential of any quinolone

derivatives. It is hoped that the model development in this di-

rection will throw new light on the anti-tuberculostatic drugdesign.



426

Table 4. Regression summary for QSARs of Quinolone compounds

R2

Molecular Descriptors M. fortuitum M. smegmatis

N = 69 ( whole set of 69 compounds)Constitutional and Geometrical Descriptors 0. 5991 0. 6265

Electrostatic Descriptors 0.6785 0.6172

Topological Descriptors 0.8357 0.8200

With all th e ab ove three sets of descrip to rs 0. 8928 0. 8932

Physicochemical Descriptors 0.6932 0.6424

N = 51 (considering C1 and N7 substitution)

Constitutional and Geometrical Descriptors 0. 5496 0. 5954





N = 48 (50% and above similarity)

Compounds: 1–8, 10–15, 18–19, 29–30,

33, 35–36, 39–63, 65–66






N = 22 (60% and above similarity)

Compounds:1, 3–5, 10–11, 14, 30, 41–42,

47–48, 52–54, 56–60, 62–63






Ref to Table 2

Acknowledgement

Payel Ghosh thanks the Council of Scientific and Indus-

trial Research, New Delhi 110001, India for the grant of

a Junior Research Fellowship to her. The authors sincerely

acknowledge the valuable comments of the anonymous re-viewers that helped to improve the quality of the final

manuscript.

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